Symmetrical property of dyadic Green´s functions for layered nonreciprocal medium

In this paper, modified symmetry relations of the DGFs are derived for the two-layer non-reciprocal anisotropic geometry shown in Fig.1. It is important to note here that the anisotropic region (Region 1) is assumed to be a non-reciprocal medium. Furthermore, two different cases are considered here as shown in Fig.1 (a) and Fig.1 (b). The first case is when the source and field points are both in the isotropic region (Region 0), and the second case is when the source and field points are in different regions (Region 0 and Region 1). We show that the interchange of the field point and the source point of the DGF for both cases is possible with the help of complimentary medium, when the anisotropic region is filled with non-reciprocal medium.